Problem: You are given an unweighted tree with n vertices. Recall that a tree is a connected undirected graph without cycles.

Your task is to choose three distinct vertices a, b, c on this tree such that the number of edges which belong to at least one of the simple paths between a and b, b and c, or a and c is the maximum possible. See the notes section for a better understanding.

The simple path is the path that visits each vertex at most once.

Input

The first line contains one integer number n (3 ≤ n ≤ 2 ⋅ 10^5) — the number of vertices in the tree. 

Next n - 1 lines describe the edges of the tree in form a_i, b_i (1 ≤ a_i, b_i ≤ n, a_i ≠ b_i). It is guaranteed that given graph is a tree.

Output

In the first line print one integer res — the maximum number of edges which belong to at least one of the simple paths between a and b, b and c, or a and c.

In the second line print three integers a, b, c such that 1 ≤ a, b, c ≤ n and a ≠, b ≠ c, a ≠ c.

If there are several answers, you can print any.

Example

Input


8
1 2
2 3
3 4
4 5
4 6
3 7
3 8


Output


5
1 8 6

Note

The picture corresponding to the first example (and another one correct answer):

<image>

If you choose vertices 1, 5, 6 then the path between 1 and 5 consists of edges (1, 2), (2, 3), (3, 4), (4, 5), the path between 1 and 6 consists of edges (1, 2), (2, 3), (3, 4), (4, 6) and the path between 5 and 6 consists of edges (4, 5), (4, 6). The union of these paths is (1, 2), (2, 3), (3, 4), (4, 5), (4, 6) so the answer is 5. It can be shown that there is no better answer.

Solution (in JAVA):

Solution:
import java.io.*;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.util.*;
public class Main {
    public static void main(String[] args) throws Exception {
        new Main().run();}

    int[] h,ne,to,wt;
    int ct = 0;
    int n;
    void graph(int n,int m){
        h = new int[n];
        Arrays.fill(h,-1);
//        sccno = new int[n];
//        dfn = new int[n];
//        low = new int[n];
//        iscut = new boolean[n];
        ne = new int[2*m];
        to = new int[2*m];
        wt = new int[2*m];
        ct = 0;
    }
    void add(int u,int v,int w){
        to[ct] = v;
        ne[ct] = h[u];
        wt[ct] = w;
        h[u] = ct++;
    }

    int color[],dfn[],low[],stack[] = new int[1000000],cnt[];
    int sccno[];
    boolean iscut[];
    int time = 0,top = 0;
    int scc_cnt = 0;

    // 有向图的强连通分量
    void tarjan(int u) {
        low[u] = dfn[u]= ++time;
        stack[top++] = u;
        for(int i=h[u];i!=-1;i=ne[i]) {
            int v = to[i];
            if(dfn[v]==0) {
                tarjan(v);
                low[u]=Math.min(low[u],low[v]);
            } else if(sccno[v]==0) {
                // dfn>0 but sccno==0, means it's in current stack
                low[u]=Math.min(low[u],low[v]);
            }
        }

        if(dfn[u]==low[u]) {
            sccno[u] = ++scc_cnt;
            while(stack[top-1]!=u) {
                sccno[stack[top-1]] = scc_cnt;
                --top;
            }
            --top;
        }
    }

    //缩点, topology sort
    int[] h1,to1,ne1;
    int ct1 = 0;
    void point(){
        for(int i=0;i<n;i++) {
            if(dfn[i]==0) tarjan(i);//有可能图不连通，所以要循环判断。
        }
        // 入度
        int du[] = new int[scc_cnt+1];
        h1 = new int[scc_cnt+1];
        Arrays.fill(h1, -1);
        to1 = new int[scc_cnt*scc_cnt];
        ne1 = new int[scc_cnt*scc_cnt];
        // scc_cnt 个点

        for(int i=1;i<=n;i++) {
            for(int j=h[i]; j!=-1; j=ne[j]) {
                int y = to[j];
                if(sccno[i] != sccno[y]) {
                    // add(sccno[i],sccno[y]);  // 建新图
                    to1[ct1] = sccno[y];
                    ne1[ct1] = h[sccno[i]];
                    h[sccno[i]] = ct1++;
                    du[sccno[y]]++; //存入度
                }
            }
        }

        int q[] = new int[100000];
        int end = 0;
        int st = 0;
        for(int i=1;i<=scc_cnt;++i){
            if(du[i]==0){
                q[end++] = i;
            }
        }

        int dp[] = new int[scc_cnt+1];
        while(st<end){
            int cur = q[st++];
            for(int i=h1[cur];i!=-1;i=ne1[i]){
                int y = to[i];
                // dp[y] += dp[cur];
                if(--du[y]==0){
                    q[end++] = y;
                }
            }
        }
    }




    int fa[];
    int faw[];

    int dep = -1;
    int pt = 0;
    void go(int rt,int f,int dd){

        int p = 0;
        stk[p] = rt;
        lk[p] = 0;
        fk[p] = f;p++;
        while(p>0) {
            int cur = stk[p - 1];
            int fp = fk[p - 1];
            int ll = lk[p - 1];
            p--;


            if (ll > dep) {
                dep = ll;
                pt = cur;
            }
            for (int i = h[cur]; i != -1; i = ne[i]) {
                int v = to[i];
                if (fp == v) continue;

                stk[p] = v;
                lk[p] = ll + wt[i];
                fk[p] = cur;
                p++;
            }
        }
    }
    int pt1 = -1;
    void go1(int rt,int f,int dd){

        int p = 0;
        stk[p] = rt;
        lk[p] = 0;
        fk[p] = f;p++;
        while(p>0) {
            int cur = stk[p - 1];
            int fp = fk[p - 1];
            int ll = lk[p - 1];
            p--;


            if (ll > dep) {
                dep = ll;
                pt1 = cur;
            }

            fa[cur] = fp;
            for (int i = h[cur]; i != -1; i = ne[i]) {
                int v = to[i];
                if (v == fp) continue;
                faw[v] = wt[i];
                stk[p] = v;
                lk[p] = ll + wt[i];
                fk[p] = cur;
                p++;
            }
        }
    }

    int r = -1;
    int stk[] = new int[200001];
    int fk[] = new int[200001];
    int lk[] = new int[200001];
    int mb = 0;
    void ddfs(int rt,int t1,int t2,int t3,int l){


        int p = 0;
        stk[p] = rt;
        lk[p] = 0;
        fk[p] = t3;p++;
        while(p>0){
            int cur = stk[p-1];
            int fp = fk[p-1];
            int ll = lk[p-1];
            p--;

            if(ll>r){
                r= ll;
                mb = cur;
            }


            for(int i=h[cur];i!=-1;i=ne[i]){
                int v = to[i];
                if(v==t1||v==t2||v==fp) continue;
                stk[p] = v;
                lk[p] = ll+wt[i];
                fk[p] = cur;p++;
            }
        }



    }

    void solve() {

        int n =  ni();
        fa =new int[n];
        faw =new int[n];

        graph(n,n-1);

        for(int i=0;i<n-1;++i){
            int u  =ni()-1;
            int v  =ni()-1;
            add(u,v,1);
            add(v,u,1);
        }
        go(0,-1,0);
        dep = -1;
        go1(pt,-1,0);
        int g = pt1;
        int all = 0;
        int from[] = new int[n];
        int z[] = new int[n];
        Arrays.fill(from,-1);


        int tot = -1;
        int mm = fa[g];
        while(fa[g]!=-1){
            all += faw[g];
            r = 0;
            mb = fa[g];
            ddfs(fa[g],g,fa[fa[g]],-1,0);
            z[fa[g]] = r;

            if(r>tot){
                tot = r;
                mm = mb;
            }


            g = fa[g];
        }

        println(all+tot);
        pt++;pt1++;mm++;
        println(pt+" "+pt1+" "+mm);

        // pt , pt1
//        int e  = pt1;
//        int st = pt1;
//        int len  = 0;
//        int len1 = 0;
//
//        int q[] = new int[n];
//        int ed = 0 ;
//        int sts = 0;
//        q[ed++]  = e;
//        int all1  = all;
//        int lst = pt1;
//        while(st!=pt) {
//            while (e!=pt && len + faw[e] - len1 <= s) {
//                len += faw[e];
//                e = fa[e];
//
//                while (ed > sts && z[q[ed - 1]] <= z[e]) {
//                    ed--;
//                }
//
//                q[ed++] = e;
//            }
//            if(e!=lst) {
//                lst = e;
//                int r = Math.max(all - len, len1);
//                if (sts < ed) {
//                    r = Math.max(r, z[q[sts]]);
//                }
//                all1 = Math.min(all1,r);
//            }
//            len1 += faw[st];
//            st = fa[st];
//            if (sts < ed && q[sts] == st) {
//                sts++;
//            }
//        }
//        println(all1);








        //N , M , K , a , b , c , d . 其中N , M是矩阵的行列数；K 是上锁的房间数目，(a, b)是起始位置，(c, d)是出口位置


//        int n = ni();
//        int m = ni();
//        int k = ni();
//        int a = ni();
//        int b = ni();
//        int c = ni();
//        int d = ni();
//
//
//        char cc[][] = nm(n,m);
//        char keys[][] = new char[n][m];
//
//        char ky = 'a';
//        for(int i=0;i<k;++i){
//            int x = ni();
//            int y = ni();
//            keys[x][y] = ky;
//            ky++;
//        }
//        int f1[] = {a,b,0};
//
//        int dd[][] = {{0,1},{0,-1},{1,0},{-1,0}};
//
//        Queue<int[]> q =  new LinkedList<>();
//        q.offer(f1);
//        int ts = 1;
//
//        boolean vis[][][] = new boolean[n][m][33];
//
//        while(q.size()>0){
//            int sz = q.size();
//            while(sz-->0) {
//                int cur[] = q.poll();
//                vis[cur[0]][cur[1]][cur[2]] = true;
//
//                int x = cur[0];
//                int y = cur[1];
//
//                for (int u[] : dd) {
//                       int lx = x +  u[0];
//                       int ly = y +  u[1];
//                       if (lx >= 0 && ly >= 0 && lx < n && ly < m && (cc[lx][ly] != '#')&&!vis[lx][ly][cur[2]]){
//                            char ck =cc[lx][ly];
//                            if(ck=='.'){
//                                if(lx==c&&ly==d){
//                                    println(ts); return;
//                                }
//                                if(keys[lx][ly]>='a'&&keys[lx][ly]<='z') {
//                                    int cao = cur[2] | (1 << (keys[lx][ly] - 'a'));
//                                    q.offer(new int[]{lx, ly, cao});
//                                    vis[lx][ly][cao] = true;
//                                }else {
//
//                                    q.offer(new int[]{lx, ly, cur[2]});
//                                }
//
//                            }else if(ck>='A'&&ck<='Z'){
//                                int g = 1<<(ck-'A');
//                                if((g&cur[2])>0){
//                                    if(lx==c&&ly==d){
//                                        println(ts); return;
//                                    }
//                                    if(keys[lx][ly]>='a'&&keys[lx][ly]<='z') {
//
//                                        int cao = cur[2] | (1 << (keys[lx][ly] - 'a'));
//                                        q.offer(new int[]{lx, ly, cao});
//                                        vis[lx][ly][cao] = true;;
//                                    }else {
//
//                                        q.offer(new int[]{lx, ly, cur[2]});
//                                    }
//                                }
//                            }
//                       }
//                }
//
//                }
//            ts++;
//        }
//        println(-1);




//        int n = ni();
//
//        HashSet<String> st = new HashSet<>();
//        HashMap<String,Integer> mp = new HashMap<>();
//
//
//        for(int i=0;i<n;++i){
//            String s  = ns();
//            int id= 1;
//            if(mp.containsKey(s)){
//                int u = mp.get(s);
//                id = u;
//
//            }
//
//            if(st.contains(s)) {
//
//                while (true) {
//                    String ts = s + id;
//                    if (!st.contains(ts)) {
//                        s = ts;
//                        break;
//                    }
//                    id++;
//                }
//                mp.put(s,id+1);
//            }else{
//                mp.put(s,1);
//            }
//            println(s);
//            st.add(s);
//
//        }

//        int t = ni();
//
//        for(int i=0;i<t;++i){
//            int n = ni();
//            long w[] = nal(n);
//
//            Map<Long,Long> mp = new HashMap<>();
//            PriorityQueue<long[]> q =new PriorityQueue<>((xx,xy)->{return Long.compare(xx[0],xy[0]);});
//
//            for(int j=0;j<n;++j){
//                q.offer(new long[]{w[j],0});
//                mp.put(w[j],mp.getOrDefault(w[j],0L)+1L);
//            }
//
//            while(q.size()>=2){
//                long f[] = q.poll();
//                long y1 = f[1];
//                if(y1==0){
//                    y1 = mp.get(f[0]);
//                    if(y1==1){
//                        mp.remove(f[0]);
//                    }else{
//                        mp.put(f[0],y1-1);
//                    }
//                }
//                long g[] = q.poll();
//                long y2 = g[1];
//                if(y2==0){
//                    y2 = mp.get(g[0]);
//                    if(y2==1){
//                        mp.remove(g[0]);
//                    }else{
//                        mp.put(g[0],y2-1);
//                    }
//                }
//                q.offer(new long[]{f[0]+g[0],2L*y1*y2});
//
//            }
//            long r[] = q.poll();
//            println(r[1]);
//
//
//
//
//        }
        //  int o= 9*8*7*6;
        //  println(o);


//       int t = ni();
//       for(int i=0;i<t;++i){
//           long a = nl();
//           int k  = ni();
//           if(k==1){
//               println(a);
//               continue;
//           }
//
//           int f = (int)(a%10L);
//           int s = 1;
//           int j = 0;
//           for(;j<30;j+=2){
//               int u = f-j;
//               if(u<0){
//                   u = 10+u;
//               }
//               s = u*s;
//               s = s%10;
//               if(s==k){
//                   break;
//               }
//           }
//
//           if(s==k) {
//               println(a - j - 2);
//           }else{
//               println(-1);
//           }
//
//
//
//
//       }

//     int m = ni();
//     h = new int[n];
//     to = new int[2*(n-1)];
//     ne = new int[2*(n-1)];
//     wt = new int[2*(n-1)];
//
//     for(int i=0;i<n-1;++i){
//         int u = ni()-1;
//         int v = ni()-1;
//
//     }
        //  long a[] = nal(n);


//        int n = ni();
//        int k = ni();
//        t1 = new long[200002];
//
//        int p[][] = new int[n][3];
//
//        for(int i=0;i<n;++i){
//            p[i][0]  = ni();
//            p[i][1]  = ni();
//            p[i][2]  = i+1;
//        }
//        Arrays.sort(p, new Comparator<int[]>() {
//            @Override
//            public int compare(int[] x, int[] y) {
//                if(x[1]!=y[1]){
//                    return Integer.compare(x[1],y[1]);
//                }
//                return Integer.compare(y[0], x[0]);
//            }
//        });
//
//        for(int i=0;i<n;++i){
//            int ck = p[i][0];
//
//        }

















    }









//    int []h,to,ne,wt;

    long t1[];
    //    long t2[];
    void update(long[] t,int i,long v){
        for(;i<t.length;i+=(i&-i)){
            t[i] += v;
        }
    }
    long get(long[] t,int i){
        long s = 0;
        for(;i>0;i-=(i&-i)){
            s += t[i];
        }
        return s;
    }

    int equal_bigger(long t[],long v){
        int s=0,p=0;
        for(int i=Integer.numberOfTrailingZeros(Integer.highestOneBit(t.length));i>=0;--i) {
            if(p+(1<<i)< t.length && s + t[p+(1<<i)] < v){
                v -= t[p+(1<<i)];
                p |= 1<<i;
            }
        }
        return p+1;
    }









    static class S{
        int l = 0;
        int r = 0 ;
        long le = 0;
        long ri = 0;
        long tot = 0;
        long all = 0;

        public S(int l,int r) {
            this.l = l;
            this.r = r;
        }
    }

    static S a[];
    static int[] o;

    static void init(int[] f){
        o = f;
        int len = o.length;
        a = new S[len*4];
        build(1,0,len-1);
    }

    static void build(int num,int l,int r){
        S cur = new S(l,r);
        if(l==r){
            a[num] = cur;
            return;
        }else{
            int m = (l+r)>>1;
            int le = num<<1;
            int ri = le|1;
            build(le, l,m);
            build(ri, m+1,r);
            a[num] = cur;
            pushup(num, le, ri);
        }
    }



    //    static int query(int num,int l,int r){
//
//        if(a[num].l>=l&&a[num].r<=r){
//            return a[num].tot;
//        }else{
//            int m = (a[num].l+a[num].r)>>1;
//            int le = num<<1;
//            int ri = le|1;
//            pushdown(num, le, ri);
//            int ma = 1;
//            int mi = 100000001;
//            if(l<=m) {
//                int r1 = query(le, l, r);
//                ma = ma*r1;
//
//            }
//            if(r>m){
//                int r2 = query(ri, l, r);
//                ma = ma*r2;
//            }
//            return ma;
//        }
//    }
    static long dd = 10007;
    static void update(int num,int l,long v){
        if(a[num].l==a[num].r){
            a[num].le = v%dd;
            a[num].ri = v%dd;
            a[num].all = v%dd;
            a[num].tot = v%dd;
        }else{
            int m = (a[num].l+a[num].r)>>1;
            int le = num<<1;
            int ri = le|1;
            pushdown(num, le, ri);
            if(l<=m){
                update(le,l,v);
            }
            if(l>m){
                update(ri,l,v);
            }
            pushup(num,le,ri);
        }
    }

    static void pushup(int num,int le,int ri){
        a[num].all = (a[le].all*a[ri].all)%dd;
        a[num].le = (a[le].le + a[le].all*a[ri].le)%dd;
        a[num].ri = (a[ri].ri + a[ri].all*a[le].ri)%dd;
        a[num].tot = (a[le].tot + a[ri].tot + a[le].ri*a[ri].le)%dd;


        //a[num].res[1] = Math.min(a[le].res[1],a[ri].res[1]);
    }
    static void pushdown(int num,int le,int ri){

    }


    int gcd(int a,int b){ return b==0?a: gcd(b,a%b);}
    InputStream is;PrintWriter out;
    void run() throws Exception {is = System.in;out = new PrintWriter(System.out);solve();out.flush();}
    private byte[] inbuf = new byte[2];
    public int lenbuf = 0, ptrbuf = 0;
    private int readByte() {
        if (lenbuf == -1) throw new InputMismatchException();
        if (ptrbuf >= lenbuf) {
            ptrbuf = 0;
            try {lenbuf = is.read(inbuf);} catch (IOException e) {throw new InputMismatchException();}
            if (lenbuf <= 0) return -1;
        }
        return inbuf[ptrbuf++];}
    private boolean isSpaceChar(int c) {return !(c >= 33 && c <= 126);}
    private int skip() {int b;while((b = readByte()) != -1 && isSpaceChar(b));return b;}
    private double nd() {return Double.parseDouble(ns());}
    private char nc() {return (char) skip();}
    private char ncc() {int b;while((b = readByte()) != -1 && !(b >= 32 && b <= 126));return (char)b;}
    private String ns() {int b = skip();StringBuilder sb = new StringBuilder();
        while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);b = readByte(); }
        return sb.toString();}
    private char[] ns(int n) {char[] buf = new char[n];int b = skip(), p = 0;
        while (p < n && !(isSpaceChar(b))) { buf[p++] = (char) b;b = readByte(); }
        return n == p ? buf : Arrays.copyOf(buf, p);}
    private String nline() {int b = skip();StringBuilder sb = new StringBuilder();
        while (!isSpaceChar(b) || b == ' ') { sb.appendCodePoint(b);b = readByte(); }
        return sb.toString();}
    private char[][] nm(int n, int m) {char[][] a = new char[n][];for (int i = 0; i < n; i++) a[i] = ns(m);return a;}
    private int[] na(int n) {int[] a = new int[n];for (int i = 0; i < n; i++) a[i] = ni();return a;}
    private long[] nal(int n) { long[] a = new long[n];for (int i = 0; i < n; i++) a[i] = nl();return a;}
    private int ni() { int num = 0, b; boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')){};
        if (b == '-') { minus = true; b = readByte(); }
        while (true) {
            if (b >= '0' && b <= '9') num = (num << 3) + (num << 1) + (b - '0');
            else return minus ? -num : num;
            b = readByte();}}
    private long nl() { long num = 0; int b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')){};
        if (b == '-') { minus = true; b = readByte(); }
        while (true) {
            if (b >= '0' && b <= '9')  num = num * 10 + (b - '0');
            else return minus ? -num : num;
            b = readByte();}}
    void print(Object obj){out.print(obj);}
    void println(Object obj){out.println(obj);}
    void println(){out.println();}
}